I forget, were the Lannisters rebuilding their fleet after the Greyjoy Rebellion? I imagine nine years is perhaps too long to rebuild the fleet to pre-rebellion strength, but I have a hard time remembering if they did any rebuilding, which seems weird considering the facts the Lannisters could easily pay for it, Tywin being Tywin, and the Lannisters history with the Ironborn in general
We don't really know, I don't believe the Lannisport fleet ever really comes up in the novel proper. That being said, we do know Tywin's personality. To Tywin, it is a big black eye that the Greyjoys successfully destroyed the Lannister fleet at anchor. That's a failure for Tywin, who has the title "Shield of Lannisport." A guy that shaves his head as soon as he goes bald is unlikely to have a visible reminder of his failure to defend Lannisport, so the Lannister navy was almost certainly rebuilt, and probably strengthened, albeit not to the level of the Redwynes, Greyjoys, or royal fleet proper. That is speculative though, I don't believe there is explicit evidence in the text.
Thanks for the question, Dreamer.
SomethingLikeALAwyer, Hand of the King










